A097345 Numerators of the partial sums of the binomial transform of 1/(n+1).

1, 5, 29, 103, 887, 1517, 18239, 63253, 332839, 118127, 2331085, 4222975, 100309579, 184649263, 1710440723, 6372905521, 202804884977, 381240382217, 13667257415003, 25872280345103, 49119954154463, 93501887462903

Offset: 0

Author

Paul Barry, Aug 06 2004

Keywords

• easy
• nonn
• frac

Comments

Numerators in the expansion of log((1-x)/(1-2x)) / (1-x) are 0,1,5,29,.. - Paul Barry, Feb 09 2005

Is this identical to A097344? - Aaron Gulliver, Jul 19 2007. The answer turns out to be No - see A134652.

From n=9 on, the putative formula a(n)=A003418(n+1)*sum{k=0..n, (2^(k+1)-1)/(k+1)} is false. The least n for which a(n) is different from A097344(n) is n=59, then they agree again until n=1519. - M. F. Hasler, Jan 25 2008

Links

• R. J. Mathar, Notes on an attempt to prove that A097344 and A097345 are identical

Crossrefs

Cf. A097344, A134652.

Programs

Mathematica

Table[ Sum[(2^(k+1)-1)/(k+1), {k, 0, n}] // Numerator, {n, 0, 21}] (* Jean-François Alcover, Oct 14 2013, after Pari *)

PARI

A097345(n) = numerator(sum(k=0,n,(2^(k+1)-1)/(k+1)))

Extensions

Edited and corrected by Daniel Glasscock (glasscock(AT)rice.edu), Jan 04 2008 and M. F. Hasler, Jan 25 2008

Moved comment concerning numerators of the logarithm from A097344 to here where it is correct - R. J. Mathar, Mar 04 2010